The cluster based optimization with the imperialist competitive algorithm of the k-traveling salesman problem

Due to the rapidly advancing technology and the increase in human needs, the importance of time in daily life is increasing day by day. In addition to meeting their needs, people aim to reach their needs as soon as possible. The Traveling Salesman Problem (TSP) is a solution problem that is used especially in logistics, transportation and product procurement areas. In this study, by creating matrices for 81 provincial coordinates and distances between cities on the map of Turkey, it was tried to find the shortest tour with the new developing Imperialist Competitive Algorithm (ICA) through these matrices. The shortest tours found with ICA were compared with the shortest tours found with Simulated Annealing Algorithm (SAA), Particle Swarm Optimization (PSO) and Ant Colony Algorithms (ACA). These comparisons are provided by the representations of the tours on the map, the total distance and travel times. In addition, due to the importance of time, more advantageous results were found by dividing these provinces into 7, 8 and 9 clusters instead of a single tour for 81 provinces. TSP analysis was performed for cluster centers and cluster inbound rounds for the formed clusters. TSP analysis was performed for cluster centers and cluster inbound rounds for the formed clusters. All these results are evaluated in terms of distances and travel times between provinces on the General Directorate of Highways page.